2/16/12
Problem Set 3
Option Pricing and Hedging
Problem 1
C(S,X,t) + B(X,t) = S + P(S,X,t)
$12 + $86
$98
$95 + $2.50
$97.50
Profit = 50 cents
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2/16/12
Problem 2
C(S,X,t) + B(X,t) = S + P(S,X,t)
$11 + $42.70
$53.70
$50+ $3
$2+ $47.44
$50+ $5
$53
$55
$49.44
Build a Box!
Problem 2
So, what comes from building the box?
Initially: $11–$3+42.70 –$2+ $5–$47.44 = $6.26
At expiration you will pay$5 no matter what
45
50
S
$50 – $45 = $5
Receive more now than you pay later!
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2/16/12
Problem 3
C(S,X,t) + B(X,t) = S + P(S,X,t)
$14.50 + $80.75
$95.25
$11.875+ $85.50
$97.375
$91.50+ $3.75
$95.25
$91.50+ $5.875
$97.375
Build a box & borrow at riskless rate
Problem 4
•  If stock goes up by $2, call will go up by
less than $2
•  The only choice that fits is answer b (rise by
$1.80)
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Problem 5
•  More time means more value for option
•  Both options have same exercise price and
same underlying asset
•  So, Option B is worth more than Option A
(choice B is correct)
Problem 6
•  For a call option, lower exercise price
means more value for the option
•  Both options have same expiration
•  So, Option A is worth more than Option B
(choice A is correct)
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2/16/12
Problem 7
•  Remember Put-Call Parity:
C(S,X,t) + B(X,t) = S + P(S,X,t)
•  This rearranges to
C(S,X,t) = S – B(X,t)+ P(S,X,t
•  If interest rate goes up, value of bond goes
down, so less would be subtacted
•  So, call premium would rise. Choice A is
correct
Problem 8
•  PV = $50 * e(-179/365*0.05) = $48.79
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2/16/12
Problem 9
•  d1 = (ln(56/48.79))/.2*sqrt(179/365) +
.5(.2*sqrt(179/365) = 1.0543
•  d2 = (ln(56/48.79))/.2*sqrt(179/365) –
.5(.2*sqrt(179/365) = 0.9142
•  Delta is 0.8541
•  Call premium is $7.84
•  Put premium is $0.6275
6